Improved loop tiling based on the removal of spurious false dependences

Abstract

To preserve the validity of loop nest transformations and parallelization, data dependences need to be analyzed. Memory dependences come in two varieties: true dependences or false dependences. While true dependences must be satisfied in order to preserve the correct order of computations, false dependences are induced by the reuse of a single memory location to store multiple values. False dependences reduce the degrees of freedom for loop transformations. In particular, loop tiling is severely limited in the presence of these dependences. While array expansion removes all false dependences, the overhead on memory and the detrimental impact on register-level reuse can be catastrophic. We propose and evaluate a compilation technique to safely ignore a large number of false dependences in order to enable loop nest tiling in the polyhedral model. It is based on the precise characterization of interferences between live range intervals, and it does not incur any scalar or array expansion. Our algorithms have been implemented in the Pluto polyhedral compiler, and evaluated on the PolyBench suite.

Variable Liberalization

“…Therefore, any removal of dependences must preserve this non-interference of live ranges to ensure correctness. This (1) non-interference of live ranges and (2) preservation of dataflow dependences form the criteria for validity of program transformation as proved in previous work [Trifunovic et al 2011;Baghdadi et al 2013]. We use this criteria to reason about correctness of the transformed program in the wake of our proposed refinement (selective removal) of dependences involving (just) temporary variables.…”

“…Live Ranges. In the context of polyhedral compilers, a live range is appropriately defined in terms of precise statement instances [Baghdadi et al 2013] instead of static statements in the program, as studied in earlier literature [Hack et al 2006]. We define live ranges as in Baghdadi et al [2013].…”

“…In the context of polyhedral compilers, a live range is appropriately defined in terms of precise statement instances [Baghdadi et al 2013] instead of static statements in the program, as studied in earlier literature [Hack et al 2006]. We define live ranges as in Baghdadi et al [2013]. A live range of a value is the range of statement instances between its definition instance and any use (Baghdadi et al [2013] explain that they consider all uses instead of the last use since loop transformations may change the last use instance).…”

“…We define live ranges as in Baghdadi et al [2013]. A live range of a value is the range of statement instances between its definition instance and any use (Baghdadi et al [2013] explain that they consider all uses instead of the last use since loop transformations may change the last use instance). However, since any source-sink pair of references can lead to as many unique live ranges as the number of iterations in enclosing loops, we represent live ranges generated by any given source-sink pair in terms of live-range "classes."…”

A Survey of Loop Parallelization: Models, Approaches, and Recent Developments

“…The conventional way to eliminate the false dependences is variable privatization and expansion, which will lead to excessive memory consumption, because both privatization and expansion are reproducing variables, the distinguish is that privatization is for each thread and expansion is for each statement instance. Recently, Baghdadi et al [35] proposed an approach to ignoring the false dependence without variable privatization and expansion. The main idea is to find the live range of temporary variables, and use the live range noninterference to relax the criterion for tiling.…”